1. MLE of the Exponential Rate For , let be i.i.d. exponential variables. a) Let be the maximum likelihood estimate (MLE) of the parameter . Find in terms of the sample mean . The subscript in is there to remind us that we have the average of values. It doesn't refer to the th sampled value . b) Use facts about sums and linear transformations to find the distribution of with little or no calculation. Recognize it as one of the famous ones and provide its name and parameters. Use it to find . c) Is an unbiased estimate of ? If it is biased, does it overestimate on average, or does it underestimate? Is it asymptotically unbiased? That is, does converge to as